Nonlinear control strategies for limiting dynamic response extremes

Under extreme environmental loadings such as winds, waves, and earthquakes, civil engineering structures are known to undergo large vibration responses, often resulting in severe damage. Recent developments in active structural control have focused on limiting the amplitude of oscillation of a structure to be within safe, allowable bounds. In this paper, a nonlinear control approach that is capable of limiting extreme dynamic responses of a structure at a reduced expense in control effort is studied. To derive the nonlinear control law, a performance index that is quartic in the states and quadratic in the control is defined. Utilizing a tensor expansion solution procedure for the resulting nonlinear optimal control problem, general polynomial representations of the nonlinear control law are obtained in illustrative problems. Numerical examples of a seismically excited, controlled structure are presented to demonstrate the ability of selected nonlinear control strategies to expend a smaller control effort than an equivalent linear control strategy while limiting the extreme displacement responses.